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Angle Sum Property of a Polygon

The following...

Question

The following figure shows a quadrilateral in which sides AB and DC are parallel. If $∠ A : ∠ D = 4 : 5, ∠ B = (3 x - 15)^{o} a n d ∠ C = (4 x + 20)^{o}$ , find each angle of the quadrilateral ABCD.

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Solution

Let $∠ A = 4 x ∠ D = 5 x S i n c e ∠ A + ∠ D = 180^{o} [∵ A B | | D C] ∴ 4 x + 5 x = 180^{o} \Rightarrow 9 x = 180^{o} \Rightarrow x = 20^{o} ∴ ∠ A = 4 (20) = 80^{o}, ∠ D = 5 (20) = 100^{o} A g a i n ∠ B + ∠ C = 180^{o} [∵ A B | | D C] ∴ 3 x - 15^{o} + 4 x + 20^{o} = 180^{o} 7 x = 180^{o} - 5^{o} \Rightarrow 7 x = 175^{o} \Rightarrow x = 25^{o} ∴ ∠ B = 75^{o} - 15^{o} = 60^{o} a n d ∠ C = 4 (25) + 20 = 100^{o} + 20^{o} = 120^{o}$ .

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Similar questions

∠ A : ∠ D = 4 : 5, ∠ B = (3 x - 15)^{\circ}

∠ C = (4 x + 20)^{\circ}

The following figure shows a quadrilateral with sides AB and DC parallel to each other.

If $∠ A : ∠ D = 4 : 5$

$∠ B = (3 x - 15)^{\circ} a n d$

$∠ C = (4 x + 20)^{\circ}$

Which of the following options is/are correct ?

In quadrilateral ABCD, side AB is parallel to side DC. If $∠ A : ∠ D = 1 : 2 a n d ∠ C : ∠ B = 4 : 5$

(i) Calculate each angle of the quadrilateral.

(ii) Assign a special name to quadrilateral ABCD.

∠ A : ∠ D = 1 : 2

∠ C : ∠ B = 4 : 5

□ A B C D

A B

D C

∠ A : ∠ D = 1 : 2

∠ C : ∠ B = 4 : 5

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